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source: code/branches/doc/src/libraries/util/Math.cc @ 7367

Last change on this file since 7367 was 7323, checked in by landauf, 14 years ago

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1/*
2 *   ORXONOX - the hottest 3D action shooter ever to exist
3 *                    > www.orxonox.net <
4 *
5 *
6 *   License notice:
7 *
8 *   This program is free software; you can redistribute it and/or
9 *   modify it under the terms of the GNU General Public License
10 *   as published by the Free Software Foundation; either version 2
11 *   of the License, or (at your option) any later version.
12 *
13 *   This program is distributed in the hope that it will be useful,
14 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
15 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
16 *   GNU General Public License for more details.
17 *
18 *   You should have received a copy of the GNU General Public License
19 *   along with this program; if not, write to the Free Software
20 *   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
21 *
22 *   Author:
23 *      Fabian 'x3n' Landau
24 *   Co-authors:
25 *      ...
26 *
27 */
28
29/**
30    @file
31    @brief Implementation of several math-functions.
32*/
33
34#include "Math.h"
35
36#include <OgrePlane.h>
37
38#include "MathConvert.h"
39#include "SubString.h"
40// Do not remove this include, it avoids linker errors.
41#include "mbool.h"
42
43namespace orxonox
44{
45#if OGRE_VERSION < 0x010603
46    /**
47        @brief Function for writing a Radian to a stream.
48    */
49    std::ostream& operator<<(std::ostream& out, const orxonox::Radian& radian)
50    {
51        out << radian.valueRadians();
52        return out;
53    }
54
55    /**
56        @brief Function for writing a Degree to a stream.
57    */
58    std::ostream& operator<<(std::ostream& out, const orxonox::Degree& degree)
59    {
60        out << degree.valueDegrees();
61        return out;
62    }
63#endif
64
65    /**
66        @brief Function for reading a Radian from a stream.
67    */
68    std::istream& operator>>(std::istream& in, orxonox::Radian& radian)
69    {
70        float temp;
71        in >> temp;
72        radian = temp;
73        return in;
74    }
75
76    /**
77        @brief Function for reading a Degree from a stream.
78    */
79    std::istream& operator>>(std::istream& in, orxonox::Degree& degree)
80    {
81        float temp;
82        in >> temp;
83        degree = temp;
84        return in;
85    }
86
87
88    /**
89        @brief Gets the angle between my viewing direction and the direction to the position of the other object.
90        @param myposition My position
91        @param mydirection My viewing direction
92        @param otherposition The position of the other object
93        @return The angle in radian
94
95        Examples:
96         - If the other object is exactly in front of me, the function returns 0.
97         - If the other object is exactly behind me, the function returns pi.
98         - If the other object is exactly right/left to me (or above/below), the function returns pi/2.
99    */
100    float getAngle(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& otherposition)
101    {
102        orxonox::Vector3 distance = otherposition - myposition;
103        float distancelength = distance.length();
104        if (distancelength == 0)
105            return 0;
106        else
107            return acos(clamp<float>(mydirection.dotProduct(distance) / distancelength, -1, 1));
108    }
109
110    /**
111        @brief Gets the 2D viewing direction (up/down, left/right) to the position of the other object.
112        @param myposition My position
113        @param mydirection My viewing direction
114        @param myorthonormal My orthonormalvector (pointing upwards through my head)
115        @param otherposition The position of the other object
116        @return The viewing direction
117
118        Examples:
119         - If the other object is exactly in front of me, the function returns <tt>Vector2(0, 0)</tt>.
120         - If the other object is exactly at my left, the function returns <tt>Vector2(-1, 0)</tt>.
121         - If the other object is exactly at my right, the function returns <tt>Vector2(1, 0)</tt>.
122         - If the other object is only a bit at my right, the function still returns <tt>Vector2(1, 0)</tt>.
123         - If the other object is exactly above me, the function returns <tt>Vector2(0, 1)</tt>.
124    */
125    orxonox::Vector2 get2DViewdirection(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition)
126    {
127        orxonox::Vector3 distance = otherposition - myposition;
128
129        // project difference vector on our plane
130        orxonox::Vector3 projection = Ogre::Plane(mydirection, myposition).projectVector(distance);
131
132        float projectionlength = projection.length();
133        if (projectionlength == 0)
134        {
135            if (myposition.dotProduct(otherposition) >= 0)
136                return orxonox::Vector2(0, 0);
137            else
138                return orxonox::Vector2(0, 1);
139        }
140
141        float cos_value = clamp<float>(myorthonormal.dotProduct(projection) / projectionlength, -1, 1);
142        float sin_value = sqrt( 1 - cos_value*cos_value );
143
144        if ((mydirection.crossProduct(myorthonormal)).dotProduct(distance) > 0)
145            return orxonox::Vector2( sin_value, cos_value );
146        else
147            return orxonox::Vector2( -sin_value, cos_value );
148    }
149
150    /**
151        @brief Gets the 2D viewing direction (up/down, left/right) to the position of the other object, multiplied with the viewing distance to the object (0° = 0, 180° = 1).
152        @param myposition My position
153        @param mydirection My viewing direction
154        @param myorthonormal My orthonormalvector (pointing upwards through my head)
155        @param otherposition The position of the other object
156        @return The viewing direction
157
158        Examples:
159         - If the other object is exactly in front of me, the function returns <tt>Vector2(0, 0)</tt>.
160         - If the other object is exactly at my left, the function returns <tt>Vector2(-0.5, 0)</tt>.
161         - If the other object is exactly at my right, the function returns <tt>Vector2(0.5, 0)</tt>.
162         - If the other object is only a bit at my right, the function still returns <tt>Vector2(0.01, 0)</tt>.
163         - If the other object is exactly above me, the function returns <tt>Vector2(0, 0.5)</tt>.
164    */
165    orxonox::Vector2 get2DViewcoordinates(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition)
166    {
167        orxonox::Vector3 distance = otherposition - myposition;
168
169        // project difference vector on our plane
170        orxonox::Vector3 projection = Ogre::Plane(mydirection, myposition).projectVector(distance);
171
172        float projectionlength = projection.length();
173        if (projectionlength == 0)
174        {
175            if (myposition.dotProduct(otherposition) >= 0)
176                return orxonox::Vector2(0, 0);
177            else
178                return orxonox::Vector2(0, 1);
179        }
180        //float angle = acos(clamp<float>(myorthonormal.dotProduct(projection) / projectionlength, -1, 1));
181
182        float cos_value = clamp<float>(myorthonormal.dotProduct(projection) / projectionlength, -1, 1);
183        float sin_value = sqrt( 1 - cos_value*cos_value );
184
185        float distancelength = distance.length();
186        if (distancelength == 0) return orxonox::Vector2(0, 0);
187        float radius = acos(clamp<float>(mydirection.dotProduct(distance) / distancelength, -1, 1)) / math::pi;
188
189        if ((mydirection.crossProduct(myorthonormal)).dotProduct(distance) > 0)
190            return orxonox::Vector2( sin_value * radius, cos_value * radius);
191        else
192            return orxonox::Vector2( -sin_value * radius, cos_value * radius);
193    }
194
195    /**
196        @brief Returns the predicted position I have to aim at, if I want to hit a moving target with a moving projectile.
197        @param myposition My position
198        @param projectilespeed The speed of my projectile
199        @param targetposition The position of my target
200        @param targetvelocity The velocity of my target
201        @return The predicted position
202
203        The function predicts the position based on a linear velocity of the target. If the target changes speed or direction, the projectile will miss.
204    */
205    orxonox::Vector3 getPredictedPosition(const orxonox::Vector3& myposition, float projectilespeed, const orxonox::Vector3& targetposition, const orxonox::Vector3& targetvelocity)
206    {
207        float squaredProjectilespeed = projectilespeed * projectilespeed;
208        orxonox::Vector3 distance = targetposition - myposition;
209        float a = distance.squaredLength();
210        float b = 2 * (distance.x + distance.y + distance.z) * (targetvelocity.x + targetvelocity.y + targetvelocity.z);
211        float c = targetvelocity.squaredLength();
212
213        float temp = 4*squaredProjectilespeed*c + a*a - 4*b*c;
214        if (temp < 0)
215            return orxonox::Vector3::ZERO;
216
217        temp = sqrt(temp);
218        float time = (temp + a) / (2 * (squaredProjectilespeed - b));
219        return (targetposition + targetvelocity * time);
220    }
221
222    /**
223        @brief Returns a unique number. This function will never return the same value twice.
224    */
225    unsigned long getUniqueNumber()
226    {
227        static unsigned long aNumber = 135;
228        return aNumber++;
229    }
230
231
232    //////////////////////////
233    // Conversion functions //
234    //////////////////////////
235
236    // std::string to Vector2
237    bool ConverterFallback<std::string, orxonox::Vector2>::convert(orxonox::Vector2* output, const std::string& input)
238    {
239        size_t opening_parenthesis, closing_parenthesis = input.find('}');
240        if ((opening_parenthesis = input.find('{')) == std::string::npos)
241            opening_parenthesis = 0;
242        else
243            opening_parenthesis++;
244
245        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis),
246                         ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
247        if (tokens.size() >= 2)
248        {
249            if (!convertValue(&(output->x), tokens[0]))
250                return false;
251            if (!convertValue(&(output->y), tokens[1]))
252                return false;
253
254            return true;
255        }
256        return false;
257    }
258
259    // std::string to Vector3
260    bool ConverterFallback<std::string, orxonox::Vector3>::convert(orxonox::Vector3* output, const std::string& input)
261    {
262        size_t opening_parenthesis, closing_parenthesis = input.find('}');
263        if ((opening_parenthesis = input.find('{')) == std::string::npos)
264            opening_parenthesis = 0;
265        else
266            opening_parenthesis++;
267
268        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis),
269                         ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
270        if (tokens.size() >= 3)
271        {
272            if (!convertValue(&(output->x), tokens[0]))
273                return false;
274            if (!convertValue(&(output->y), tokens[1]))
275                return false;
276            if (!convertValue(&(output->z), tokens[2]))
277                return false;
278
279            return true;
280        }
281        return false;
282    }
283
284    // std::string to Vector4
285    bool ConverterFallback<std::string, orxonox::Vector4>::convert(orxonox::Vector4* output, const std::string& input)
286    {
287        size_t opening_parenthesis, closing_parenthesis = input.find('}');
288        if ((opening_parenthesis = input.find('{')) == std::string::npos)
289            opening_parenthesis = 0;
290        else
291            opening_parenthesis++;
292
293        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis),
294                         ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
295        if (tokens.size() >= 4)
296        {
297            if (!convertValue(&(output->x), tokens[0]))
298                return false;
299            if (!convertValue(&(output->y), tokens[1]))
300                return false;
301            if (!convertValue(&(output->z), tokens[2]))
302                return false;
303            if (!convertValue(&(output->w), tokens[3]))
304                return false;
305
306            return true;
307        }
308        return false;
309    }
310
311    // std::string to Quaternion
312    bool ConverterFallback<std::string, orxonox::Quaternion>::convert(orxonox::Quaternion* output, const std::string& input)
313    {
314        size_t opening_parenthesis, closing_parenthesis = input.find('}');
315        if ((opening_parenthesis = input.find('{')) == std::string::npos)
316            opening_parenthesis = 0;
317        else
318            opening_parenthesis++;
319
320        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis), ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
321        if (tokens.size() >= 4)
322        {
323            if (!convertValue(&(output->w), tokens[0]))
324                return false;
325            if (!convertValue(&(output->x), tokens[1]))
326                return false;
327            if (!convertValue(&(output->y), tokens[2]))
328                return false;
329            if (!convertValue(&(output->z), tokens[3]))
330                return false;
331
332            return true;
333        }
334        return false;
335    }
336
337    // std::string to ColourValue
338    bool ConverterFallback<std::string, orxonox::ColourValue>::convert(orxonox::ColourValue* output, const std::string& input)
339    {
340        size_t opening_parenthesis, closing_parenthesis = input.find('}');
341        if ((opening_parenthesis = input.find('{')) == std::string::npos)
342            opening_parenthesis = 0;
343        else
344            opening_parenthesis++;
345
346        SubString tokens(input.substr(opening_parenthesis, closing_parenthesis - opening_parenthesis), ",", SubString::WhiteSpaces, false, '\\', true, '"', true, '\0', '\0', true, '\0');
347        if (tokens.size() >= 3)
348        {
349            if (!convertValue(&(output->r), tokens[0]))
350                return false;
351            if (!convertValue(&(output->g), tokens[1]))
352                return false;
353            if (!convertValue(&(output->b), tokens[2]))
354                return false;
355            if (tokens.size() >= 4)
356            {
357                if (!convertValue(&(output->a), tokens[3]))
358                    return false;
359            }
360            else
361                output->a = 1.0;
362
363            return true;
364        }
365        return false;
366    }
367}
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